The extracavity pumped dual-wavelength Raman laser based on the main and the secondary Raman shifts of Raman crystal was theoretically analyzed. From the wave equation of the light field and the damped harmonic oscillator wave equation for the vibrational wave in Raman crystal, a group of coupled wave equations were deduced to describe the fundamental laser, Raman laser 1 and Raman laser 2 were then derived. The coupled wave equations were normalized by introducing several normalized parameters. The effects of the normalized Raman gain coefficient, normalized fundamental pulse width and output mirror reflectivities on the performance of extracavity dual-wavelength Raman lasers were numerically analyzed. It is found that selecting the output mirror with reflectivity less than 0.5 for the main frequency shift and larger than 0.5 for the secondary frequency shift, and the Raman crystal with small difference gain coefficients of the two Raman modes, and properly increasing the pulse width of the incident fundamental frequency light can improve the conversion efficiency of the secondary Raman frequency shift and achieve effective dual wavelength operation. The theoretical derivation and numerical calculation of this paper can be used as a theoretical tool for the design and analysis of extracavity dual-wavelength Raman lasers, and can provide a reference for the experimental research of this kind of lasers.